Convexity properties

of holomorphic mappings in

Authors:
Kevin A. Roper and Ted J. Suffridge

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1803-1833

MSC (1991):
Primary 32H99; Secondary 30C45

Published electronically:
January 26, 1999

MathSciNet review:
1475692

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Not many convex mappings on the unit ball in for are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the ``Quasi-Convex Mappings, Types A and B'' seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.

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Additional Information

**Kevin A. Roper**

Affiliation:
Department of Mathematics, Munro College, P.O., St. Elizabeth, Jamaica

**Ted J. Suffridge**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Email:
ted@ms.uky.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02219-9

Keywords:
Convex,
holomorphic mapping,
dimension $n$

Received by editor(s):
July 10, 1995

Received by editor(s) in revised form:
August 11, 1997

Published electronically:
January 26, 1999

Article copyright:
© Copyright 1999
American Mathematical Society